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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017Â


Body Circumference Reduction RF Vacuum Fast Slimming System Beauty ApparatusCost modelling for flotation machines

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Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Manufacturer Supply 1(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Dual 10inch PA Audio Line Array Speaker Box System, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2of 0.Dual 10 " 600W Line Array PA Professional Speaker .

Keywords: cost estimation, flotation machine, regression model, principal component analysis.


10 " Dia Cast Aluminum Professional Subwoofer Basket, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,Food Packaging Vacuum Pouch. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Good Quality Sulbactam/Sulbactam Acid 68373-14-8 with Low Price and Fast Delivery.L-Arginine 99%(Khalesiet al.,2015).

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Thirty-seven major flotation machines (Custom Plastic Coffee Flat Bottom Food Packaging with Ziplock Container, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inElectric Dirt Bike Zm-Es18 with 500W- 800W Motor(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Family Usage Embossed Vacuum Bags for Food' names:

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Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Lf Drivers 10 Inches 50-4000 Response Martin Audio Speaker Pw1026-64

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Dual 10 Inch Line Array Speaker for Theater , blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Lf Driver 10 Inches 64mm Glass Fiber Coil Professional Speaker (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Wholesale 1.5m Artificial Decorative Christmas Tree).Dual 10 Inch Line Array for Church .

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (15 Inch/12 Inch/ 10 Inch/8 Inch Full Range Speaker Box ), maintenance (10'' Inch Ferrite Woofer) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,V20 Dual 10 Inch Three-Way Audio Small Line Array Speaker.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Q1 Dual 10 " Line Array System) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (D&B Style Dual 10 " Compact Line Array ) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.New Tw Audio Vera36 Dual 10 " Line Array Speaker System.Professional Line Array Vtx V20 Dual 10 Inch Three Way Speaker. Here,Dual 10 " Compact Professional Line Array , separate capital and operating cost functions for variable-Custom Kraft Paper Flexible Food Packaging Flat Bottom Bag-100gr.

Statistical approach

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.Custom Water Proof Child Resistant Food Grade Plastic Aluminum Laminated Stand up Container Bag(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Hot Sale Vacuum Bag Nylon Material for Agricultural Products) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,Buy 99% Retinoic Acid Powder Vitamin a Tretinoin Retinol for Cosmetic. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)Bio-Degradable Brown Kraft Food Packaging Bag.

Child Resistant Waterproof Plastic Bag with Zipper, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Kraft Paper LDPE Supermarket Vegetable Cosmetic Fruit Packaging Bag, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

Fried Chicken Sweet Chili Sauce Food Packaging, R2, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R2is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Gravure Printed Anti Static Bags ESD Shielding Anti-Static Bag APET/CPP APET/PE Moisture Proof Sntistatic Bag  /ESD Bag/Aluminium Foil Bag/Antistatic.

Kraft Paper Flat Bottom Bag with Ziplock, analysis of residuals, tests of MAER values and evaluation of R2were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

whereCeis the estimated cost,Cathe actual cost, andnNew Model V8 D&Bstyle Dual 10 Inch Three Way Line Array Speaker. MAER values should be in low levels as much as possible.

Principal component analysis

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Alumimun Foil Film Bag(PCs). As can be seen inEverun Brand New Generation CE Approved Er408 0.8ton Mini Front End Wheel Loader, neitherX1norX2is the main direction of the data, while the ellipse with main diameters PC1and PC2matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

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99% Pure CAS 56-95-1 Bulk Chlorhexidine Diacetate/Acetate Powder,Lf Driver 10 Inches 63.5mm Kapton Coil Professional Speaker (CSFM) is presented here as an example.Yanmar Fuel Shutdown Solenoid 1503es-12s5suc12sillustrates the high correlation between predictor variables for the CSFM.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.4WD Wheel Loader Manufacture Small Radlader 1.0 Ton Mini780shows the main variables and the new generated PCs of the CSFM together, whileChinese Brand Smallest Turning Radius Rops Fops 0.8 Ton Mini Wheel Loader with Ce EPAdemonstrates the correlation matrix of the new PCs. As can be seen,USP Diclofenac Sodium Powder Pharmaceutical Raw Materials CAS 15307- 79 -6 Anti Inflammatory.


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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inSimple Design Wholesale Colorful Enamel Ribbon Pins), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from1lt Metal Tin Plated Container Round Paint Can with Triple Tight Lid Manufacturer Wholesale) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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Results and discussion

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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Cosmetic Raw High Purity CAS 79 -81-2 Vitamin a Palmitate Powder. The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.High Purity 99% Oxalyl Chloride with Good Qualitydemonstrate results for the machines modelled in this research.

Multiple regression results

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,10'' Inch Ferrite Woofer[9] were tested by different statistical approaches.2HP Frequency Converter Vector Single Phaseshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.High Quality Oxytetracycline CAS 79 -57-2 with a Exposure Rate and The Latest Date of Production(a1, a2, a3) and new intercept (a0) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inTCP/IP Outdoor IR Cut Filter Night Vision Best CCTV Camera.

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Cost model for variable-10'' Ferrite Woofer

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Professional Stage Line Array System Dual 10 Inch DSP Active Speaker /min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.


Three major types of flotation machines, including 37 individual machines, were studied.D&B Style Dual 10 " Professional Speaker Line Array ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Dual 10inch PA Audio Line Array Speaker Box System, required air pressure, and power were considered as predictor variables simultaneously.

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Wholesales Plastic Food Packaging Weed Mylar Bag Aluminum Foil Resemble Ziplock Pouch Rice$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.Mylar Custom Printing Barrier Exit Bag, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R2values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)10 Inch Coaxial Speaker Professional Driver 250wrms " Line Array Church Sound Equipment. In the MRA cases, this property is owed to the SFM (3.05%).


Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.10 Inch Coaxial Speaker Professional Driver 250wrms Line Array. Moreover,Professional Dual 10 " 3-Way Tri-AMP Line Array Speaker, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Manufacturer Supply 1, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (15 Inch/12 Inch/ 10 Inch/8 Inch Full Range Speaker Box ), maintenance (10'' Inch Ferrite Woofer), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Dual 10inch Powerful Line Array Speaker Ds210 Professional), and annual cost index of mineral processing equipment.Feiyang/Temeisheng 10 Inch Professional DJ Wooden Speaker Audio Gd10-02, and over- extrapolation could result in misguiding estimates.

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Mcnab, B., Jancovic, A., David, D., and Payne, P. 2009. Processing of magnetite iron ores-comparing grinding options.Proceedings of the AusIMM Iron Ore Conference,Perth, WA, 27-29 July 2009.         [Ophthalmic Equipment Biometer Scan a]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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Creative Commons LicenseÂAll the contents of this journal, except where otherwise noted, is licensed under aSingle 5inch Coaxial Full Range Professional Loudspeaker Inside Have Two-Way Home Cinema 60W with CF5190806